Relativity and Magnetism

I understand that the the speed of electrons in a wire along with the coulomb attraction accounts for the attraction of two wires carrying current in the same direction and the repulsion of two wires carrying current in the opposite direction; however, I'm having trouble visualizing this.

If I am in the laboratory frame of reference, the electrons are moving with respect to me and the atoms with their positive charges are still. Now the electrons will shrink in size and be compressed into a smaller length giving the wire a net negative charge per unit length. Since both wires are carrying the same current and behave the same relative to me, both wires will have a net negative charge and both will repel each other. This is obviously independent of which direction the currents are going.

For two beams of equal-charge particles (electrons) moving in the same direction, the Coulomb forces between the two beams repels the particles in the other beam. The Lorentz v x B force between the two beams attract. These two opposing forces are equal at very relativistic velocities. For currents in wires, there is no Coulomb force.